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It can be confusing to keep mean, median, and average apart. Let's use the same example of the income of the people of the United States. The mean income of the people tells us something about the largest group within the United States. So if the middle class is the largest group in our society then the mean would be the number that belongs to that group. It is kind of a crude number.

The average income of people in the United States is found by adding all incomes and then dividing that by the number of people who earned income. This is a very precise number, but the average may not always give us good information, for instance, when one person makes a whole lot more money than the others then the outcome is skewed. If 9 people earn $10,000 (total $90,000) and one person makes eleven times as much ($110,000) then together these ten people make $200,000. If we divide this number by ten then the average each person makes is $20,000. This is twice as much as nine out of the ten are making. In this case the average is off by a lot because a single person made so much. Normally, the average gives us a good idea, but as this example shows the average can sometimes be tugged towards a much higher or lower outcome. Do you know what the mean would be for this group? (Answer: the largest group are the nine people making $10,000 each, so that would be the answer.)

The median income is the very specific income the person in the middle makes. Let's quickly add an eleventh person to the ten we talked about above, an eleventh person who made $12,000. We then line up all eleven people, and look for the person in the middle: number 6 (with five people on the left and five people on the right). Then we know that the median is $10,000 because that is what number 6 earns. In this example a large group of people made the same amount of money. In real life people's income are scattered all over the map, so the person in the exact middle would deliver good information, while in a sense the average income would also deliver good information.
When we would compare both median and average numbers for, for instance, the United States and Germany, then the outcome could be that the average income in the United States is higher than the average income in Germany, while the median income in the United States is lower than the median income in Germany. The average number indicated how much we all make together, while the median tells us something about the exact income the person in the middle of society is making. The person in the middle in Germany may make more than the income of the person in the middle in the United States.

Now let's do it all again but this time with different examples.

Mean: if I have ten red balls, seven green balls, three blue balls, and two yellow balls, then the mean is red (because the largest group is the group of the red balls, and yes, it is a crude measure).

Average: if there are two people of five feet tall, one of six, and two of seven feet tall, then the average is 6 feet.

Median: If there is one person of 150.8 pounds, one of 165.2 pound, one of 174.5 pound, one of 185 pound, and one person of 350.1 pounds, the median weight is 174.5 (it is the exact specific information of the person in the middle).

Poverty: the international way to measure poverty is to look at what the person in the exact middle of a society makes and half that amount is the poverty threshold. Understand that this is not 25%, but half of a very specific amount of money. If all income earners are lined up, and the person in the exact middle earns $38,447,50 then the poverty threshold would be $19,223,75 If you make less than that amount you are then considered to live in poverty. Again, these figures are not the correct figures, they are just used for this example.

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